In the field of communications, information is often encoded into a large spectrum of analog signals and transmitted to receivers where the information is subsequently extracted. The spectrum typically is made up of many channels, each channel carrying a distinct envelope of information. A channel is defined as a group of frequencies having a certain bandwidth (b.sub.0) that are centered about a center frequency (f.sub.0). FIG. 1 illustrates a typical signal a(t) having many channels 10. Once the spectrum of signals is transmitted, a channel is selected and isolated so that the encoded information within the channel may be extracted.
One manner of implementing a receiver for selection of a particular channel (also referred to as the channel of interest) is to first shift a(t) such that the center frequency of the channel of interest is centered at a first intermediate frequency f.sub.i1. Next, the shifted signal a(t) is passed through an analog filter which isolates several channels (including the channel of interest and other unselected channels) from signal a(t). The signal resulting from this step is then shifted again to a second intermediate frequency f.sub.i2 by a complex mixer.
The complex mixer generates an analog signal having real (I) and imaginary (Q) components, each component having the channel of interest centered at f.sub.i2. In order to generate this complex signal, the complex mixer is implemented with two matched mixers; one for generating the real shifted component and one for generating the imaginary shifted component.
Each of the real and imaginary components of the complex signal generated by the mixer is coupled to one of a pair of matched analog-to-digital (ND) converters which function to convert the real and imaginary components of the complex analog signal into real and imaginary components of a complex digital signal.
At this point in signal processing, it is desired to perform a final digital filtering step so that the channel of interest may be isolated from the rest of the unselected channels. However, due to mismatches in components in the imaginary and real signal processing paths of the analog mixers and ND converters in the above implementation of the receiver, each of the channels (including the channel of interest) in the complex digital signal has been contaminated by the other. For instance, the digital signal representing the channel of interest constitutes an uncontaminated component and an error component associated with the other unselected channels. Similarly, the digital signal representing each of the unselected channels has an uncontaminated component and an error component associated with all of the other channels (including the channel of interest). Consequently, if the complex digital signal is passed through a digital filter to isolate the channel of interest, the information decoded from the channel of interest would be inaccurate since it includes information from other adjacent channels.
One common prior art filter (referred to as a Weiner filter) used for overcoming contamination problems functions to remove (or decorrelate) a contaminating signal from a contaminated signal. Generally, the Weiner filter functions such that given a contaminated signal and the signal that contaminated it (i.e. the contaminating signal), the Weiner filter estimates how much of the contaminating signal is in the contaminated signal and subtracts exactly that amount leaving only the desired decorrelated signal. The Weiner-type of filter is only effective if the original contaminating signal is known and is not contaminated by any other signal.
In the receiving method described above in which a signal having multiple channels is passed through a series of filters, mixers and ND convertors, each channel contaminates the other. Thus, the contaminating channel is not known since it too is contaminated. As a result, the Weiner filter becomes ineffective since it requires that the original contaminating signal be known. Consequently, what is needed is a method of decorrelating a signal having two mutually contaminated channels.